Question

Given (5,-12) is a point on the following line, convert the equation to point-slope form.

6x+ 2y = 6
A. y - 12 = -6(x - 5)
B. y + 12 = -6( – 5)
C. y + 12 = -3(x – 5)
D. y - 12 = -3(x - 5)

Answer 1

C

Explanation:

Slope = - 3

y - (-12) = -3(x - 5)

y + 12 = -3(x-5)

Answer 2

C. y + 12 = -3(x – 5)

Explanation:

The point-slope form is

`y-y_(1)=m(x-x_(1))`

To express a line in the point-slope form, we actually its slope and a point that the line crosses. According to the problem, the point is
`(5,-12)`.

The slope we can find it from the expression that gives us the problem

`6x+2y=6`

We are gonna express this equation in an explicit form, which is gonna give us the slope. Remember that in explicit form, the slope is the coefficient of the x-variable.

`2y=6-6x\\y=(6-6x)/(2)\\ y=3-3x`

As you can observe, the slope is -3.

Now, using all this information, we can find the point-slope expression

`y-y_(1)=m(x-x_(1))\\y-(-12)=-3(x-5)\\y+12=-3(x-5)`

If we compare, we deduct that the correct answer is C., because is the same expression that we have.